OK...where to begin...
Smoke ring, as we call it, is formed from nitric oxide (not to be confused with nitrous oxide) in the smoke chamber, which reactes with myoglobin in the meat to form a coloring or pigment called nitrosohemochrome.
Though we may like to think that this all happens from the smoke woods alone, it does not. As many have stated about electric smokers, smoke rings will be faint and shallow, if not non-existent. A gas or solid fuel heated smoker will generate a smoke ring in meats with or without the use of smoke wood. Yes, you can create a smoke ring without smoke woods as I have demonstrated on a few ocassions.
I have found that if I want to optimize the reaction with nitric oxide using a propane or charcoal cooker (grill or smoker) I start with a cold chamber, building the temps up gradually over a period of anywhere from 20-60 minutes, depending on the weight and type of meat or poultry I'm smoking. Using this method allows the meat to react over a longer period of time until the sub-surface temperatures of the meat begin to rise above the point at which the reaction begins to slow and eventually stop all together.
Though this may not be a recommended method by most experienced smokers for reasons of food safety (guidelines for intact whole muscle vs non-intact whole muscle in specific), and I wouldn't recommend it myself without instruction as to monitoring chamber temps, time and internal meat temps closely, I have used this method with repeatable results. Hands down, everytime I've used this method, I get deep reactions in the meat. On my last brisket point smoke, the beef had 3/8 to 1/2" depth of the reaction, and this was with a cold start leading to 200* chamber temps initially, while holding approx, 220* for the majority of the remainder of the smokiong time. I monitored internal temps, and my initial internal temp reading was 140* @ 3-hrs, 20-min into the smoke, so food safety wasn't an issue. And, this smoke was done in a propane fired smoker.
That said, I will tell you the only things I know of which have hindered the reaction in meats from my own personal experience:
1) excessive humidy in the smoke chamber;
2) useing a cooking grate which rests directly over a water pan...this casues the meat to steam and will cause limited exposure to nitric oxode as a result;
3) excessively high smoke chamber temps during the inital stages of smoking;
4) external fat on the meat, which prevents nitric oxide reaction by keeping it from contacting the meat;
5) EDIT: skin on poultry, which also prevents the meat from contacting nitric oxide.
I have not personally used an electric smoker, but as I've read in other threads, may not be easily achieved, if at all.
If you care to observe my latest findings regarding the above methods in which I utilized measures to ensure that items 1 thru 4 would not prevent a good smoke ring in my meat, feel free to have a look HERE.